compute_eta
===========

.. py:function:: t3toolbox.backend.probing.compute_eta(down_tt_cores, mus, nus)

   .. code-block:: python

      def compute_eta(
              down_tt_cores:         typ.Union[typ.Sequence[NDArray], NDArray], # len=d. elm_shape=C+(rLi,nOi,rR(i+1))
              mus:                    typ.Union[typ.Sequence[NDArray], NDArray], # len=d. elm_shape=W+C+(rLi,)
              nus:                    typ.Union[typ.Sequence[NDArray], NDArray], # len=d. elm_shape=(...,rR(i+1))
      ) -> typ.Union[typ.Sequence[NDArray], NDArray]: # etas. len=d, elm_shape=W+C+(nOi,)


   Compute downward edge variables associated with edges between Tucker cores and adjacent TT-cores.
   Used for probing a Tucker tensor train.

   See Section 6.2, particularly Figure 7 and Algorithm 5, in:
       Alger, N., Christierson, B., Chen, P., & Ghattas, O. (2026).
       "Tucker Tensor Train Taylor Series."
       arXiv preprint arXiv:2603.21141.
       `https://arxiv.org/abs/2603.21141 <https://arxiv.org/abs/2603.21141>`_